Improving Time and Memory Efficiency of Genetic Algorithms by Storing Populations as Minimum Spanning Trees of Patches

In many applications of evolutionary algorithms the computational cost of applying operators and storing populations is comparable to the cost of fitness evaluation. Furthermore, by knowing what exactly has changed in an individual by an operator, it is possible to recompute fitness value much more efficiently than from scratch. The associated time and memory improvements have been available for simple evolutionary algorithms, few specific genetic algorithms and in the context of gray-box optimization, but not for all algorithms, and the main reason is that it is difficult to achieve in algorithms using large arbitrarily structured populations. This paper makes a first step towards improving this situation. We show that storing the population as a minimum spanning tree, where vertices correspond to individuals but only contain meta-information about them, and edges store structural differences, or patches, between the individuals, is a viable alternative to the straightforward implementation. Our experiments suggest that significant, even asymptotic, improvements -- including execution of crossover operators! -- can be achieved in terms of both memory usage and computational costs.